1833
SOMESTUDIESOF DIAMOND GROWTH RATES transfer and hydrogen-bonding effects on the glass transition in aqueous systems. These interesting results will be discussed in a future paper.
Acknowledgment. We wish to thank the Office of Saline Water, U. S. Department of the Interior, for their support of this project.
Some Studies of Diamond Growth Rates by R. H. Wentorf, Jr. General Electric Research and Development Center, Schenectady, N e w Yorlc 12601
(Received November 50, 1970)
Publication costs assisted by the General Electric Co.
Carbon can be transported along a temperature gradient in a bath of molten catalyst metal such as iron, nickel, etc. When the bath is essentially saturated with carbon at pressures high enough for diamond stability, diamond can dissolve from a source in a region at a higher temperature and crystallize on a diamond seed crystal in a region at a lower temperature. In this way the diamond growth process may be somewhat regulated and studied by controlling the carbon flux and bath characteristics. The crystals grow layer by layer and impurities may be trapped under rapidly advancing layers. The rate of desorption of impurities controls some growth. Sometimes graphite or spurious diamond crystals may form. Gravity also affects the operation of the process.
A. Introduction During the past few years the continuing development of high-pressure, high-temperature techniques has permitted the controlled growth of diamond over long periods of time, e.g., 1 week. It has thus become possible to grow good quality crystals of sizes up to about 5 mm (1 carat) and to study growth rates, growth mechanisms, the incorporation and effects of impurities, etc. This paper and the one by Strong and Chrenko which follows it describe some of the methods and results of this work. In this work we generally used diamond as the source of carbon. By contrast, nowadays most synthesized diamonds are grown from graphite or similar forms of carbon. Typical operating ranges for diamond growth are indicated by the diagonally striped region in Figure 1. At the synthesis pressures, diamond is the stable form, and with the help of catalyst metals such as iron, nickel, etc., it crystallizes in various habits and a t rates determined by both the local pressure and the temperat ~ r e . l - ~ The actual transformation takes place through a thin metal film and is difficult to control, especially for long periods of time. Several years ago Strong and Tuft4 used this process to make onionlike diamonds of 1 to 3 carat size by growing successive layers of new diamond on a seed crystal, but each layer of growth required a separate run a t high pressure, and the method was slow and tricky. Many inclusions were trapped between the layers of growth so that the diamonds, though large, were not particularly beautiful
nor useful. At that point it seemed appropriate to look more at slightly different diamond-growing methods. Laboratories rich in diamonds might consider using diamond as a source of carbon for growing diamonds. One possible method is indicated in Figure 1. Diamond is supposed to dissolve in a hot region and crystallize in a cool region of a suitable bath. The entire system is at diamond-stable pressure and the driving force for recrystallization is provided by the solubility difference resulting from the temperature difference. I n principle this process ought to be easier to control than when diamond forms from graphite under the combined influences of both temperature and pressure. Our early experiments along this line were only partially successful; i e . , the diamond dissolved well enough, but graphite crystallized instead, due to kinetic factors, even though thermodynamic considerations forbade it. However, diamond seed crystals placed in the cool region often grew larger. (This tendency for graphite to appear where it is not stable can be observed at pressures as high as 140 k b a r ~ . ) ~ ! ~ (1) H.P.Bovenkerk, F. P. Bundy, H. T . Hall, H. M. Strong, and R. H. Wentorf, Jr., Nature, 184, 1094 (1959). (2) H. E’. Bovenkerk, Progr. V e r y High Pressure Res., Proc. I n t . Conf., 58 (1961). (3) R. H. Wentorf, Jr., Advan. Chem. Phys., 9, 365 (1965). (4) H.M.Strong and R. E. Tuft, private communication. (5) F. P. Bundy, J . Chem. Phys., 38, 631 (1963); Science, 137, 1057 (1962). (6) R. H. Wentorf, Jr., Ber. Bunsenges. Phys. Chem., 70, 975 (1966).
T h e Journal of Physical Chemistry, Voi. Y 6 , N o . 12, 1971
1834
R. H. WENTORF,JR.
PRESSURE, KB.
END DISC INSULATION
701-
CATALYST
(a SE:E
CARBON SUPPLY INSULATION HEATER TUBE CARBON SUPPLY CATALYST
50-
SEED BED TEMPERATURE,
'K
Figure 1. A portion of the pressure-temperature phase diagram for carbon. 1
I
I
I
Ni.C 57kb
1700
Figure 3. High-pressure cell for diamond growth.
The nutrient carbon, usually a densely packed mixture of diamond and graphite, occupies the hotter midlength region. (The graphite changes to diamond early in the operating period and is added to increase the average density of the starting mixture so as to minimize cell distortion and pressure loss.) Two cooler regions, one near each end of the cell, are available for diamond growth out of the catalyst metal baths, and diamond seed crystals are placed at these cool ends. After the cell is assembled and piaced in the pressure apparatus, it is compressed to the desired operating pressure, usually around 55-60 kbars, and then heated to bring the midlength to say 1450" and the seed regions typically to about 1420". Thermocouples may be used to monitor the cell temperatureslO and to detect significant pressure changes within the cell.
C. Results and Discussion 1 . Transient States and Seeds. While the cell is
4.7
9.0
13.15
I6 7 AloC
Figure 2. The nickel-carbon phase diagram at 57 kbars, according to Strong and Hanneman.7J
Figure 2 is a nickel-carbon phase diagram at 57 kbars, as worked out by Strong and Hanneman.'~~Here one can see how the solubilities of diamond in nickel, and of nickel in diamond and graphite, vary with temperature. A temperature interval of about 60" is available for dissolving and crystallizing diamond a t this pressure in this system. Actually only practical considerations, such as growth rate or insulation failure, prevent the use of arbitrarily high temperatures for dissolving the carbon from diamond or graphite, but of course the diamond must crystallize where it is stable.
B. Experimental Techniques A convenient way to study these systems is t o arrange the carbon and catalyst metal as indicated in Figure 3. This reaction cell can be compressed in a "Belt" highpressure a p p a r a t u ~ . ~ The heat generated in the carbon tube resistance heater flows out of the cell in such a way that useful axial temperature gradients exist in the tube. The Journal of Physical Chemistru, Vol. 76, N o . 19, 1971
warming up, several interrelated phenomena occur which stem from carbon flux and gravity. The solubility of carbon in say the nickel-carbon or iron-carbon eutecticis higher at 55 kbars than at 1 atme6t7 Therefore, even a bath which is made of metal saturated with carbon at 1 atm will not be saturated with carbon when it melts in the reaction cell. The extra carbon is supplied from the nutrient carbon and also from the seeds. The density of the bath falls with increasing carbon concentration. During the initial heating period the top bath (Figure 3) stirs itself by convection from the thermal and carbon concentration gradients, and carbon from the nutrient mass rapidly saturates the entire molten bath. In the bottom bath the main temperature and carbon concentration gradients act to oppose convection, and carbon from the nutrient mass moves downward into the bath by the relatively slower process of diffusion. An hour or more may be required to reach a steady state there, according to our studies. (7) H. M. Strong, Acta Met., 12, 1411 (1964). (8) H. M. Strong and R. E. Hanneman, J. Chem. Phys., 46, 3668 (1967).
(9) H. T. Hall, Rev. Sci. Instrum., 31, 125 (1960). (10) R. E. Hanneman and H. M. Strong, J. Appl. Phys., 36, 523 (1965); 37, 612 (1966).
SOME STUDIES OF
DIAMOND GROWTHRATES
Archimedes' principle still operates a t very high pressures, and many substances including diamond and graphite float in the metal bath. The central nutrient mass remains in place by virtue of its rough surface against the container walls, but a few crystals of diamond which are loosened by dissolution may float u p ward to the cool end of the top bath to become visiting seed crystals. Thus the top bath rarely starves for seeds. The cool end of the bottom bath is more suitable for growing only a few crystals because both seed and impurity populations tend to be lower there. The seed crystals are mechanically embedded in the bottom insulation so that they and any new growth upon them will not float up and dissolve. The problem is to have suitable seeds available when the steady state is finally reached. If the seed is too small or too exposed to the bath, it may dissolve entirely or float away during warm-up, and if no seeds remain, diamond growth, if any, will be erratic and based on diamond made in situ from precipitated graphite or diamonds nucleated spontaneously by a large carbon supersaturation. On the other hand, if the seed is too large, the new growth tends to be of poor quality because a relatively large, necessarily etched seed surface bears many active growth sites which, like barnacles on a ship, do not usually act in harmony. Extremely small variations in bath compcsition as well as the etching of the seed during warm-up ensure that a large crystal which is grown in one experiment will not be a flawless seed for the bath in a second experiment. Each crystal is an individual, with its own faults, adjusted to its environment, and the same crystal may not fare well in a slightly different environment. The etching problem would not be bothersome if something besides diamond (or graphite newly converted to diamond in situ) could be used as seeds, but so far only diamond has been found to be effective.' 2. Carbon Transport. In a given catalyst-metal system, the flux of carbon depends mainly upon the temperature gradient and can be estimated from the total amount of carbon found to be transported to the cool end in a known time interval. In the top bath, thermal convcction aids diffusion, and carbon fluxes of 3 X lo-' g sec-' em-* or more are observed with temperature gradients of about 100" cm-'. In the bottom bath the temperature gradient does not favor convection and the carbon fluxes are about lo-' g sec-I em-* through the liquid. It is easy to maintain carbon fluxes greatly in excess of what growing crystals can accommodate. S. Nucleatia. If the diamond nuclei present are kinetically unable to absorb the imposed carbon flux, graphite nucleates spontaneously, despite its thermodynamic instability, and g r o w as large, shiny flakes.' In the immediate vicinity of a diamond crystal grown well within the range of diamond stability no graphite ie found, as shown in Figure 4. Here one looks at the
183.5
cool end of an iron bath. The diamond crystal resting on the circular surface \\'as pried from t Iic? cavity near it. Figure 5 shows a prolific seedbed of diamond which, by virtue of its many active growth sitrs and large area, WI.$ able to accept as diamond all the carbon fed to it. One notes that certain crystals, nsually twins, The Journolo/Ph~aicolChmialru. Vol. 76. Yo. 1% 1971
R. H. WENTORF.JR.
1836
grow faster than others, and, like the tallest trees in a forest, shadow their fellows. It is possible for graphite which has been deposited from solution to change into diamond. This change is favored by higher operating pressures or by thermal cycling which may stress the graphite mechanically or produce a temporary supersaturation great enough to form locally imperfect graphite which is more easily converted to diamond because of its greater thermcdynamic instability. 4. Crystal Grntulh. The diamond growth process appears to take place as follows. First, a tiny patch of a new layer-one might call it a “layer nucleus”forms on say a crystal edge. Second, the layer spreads out as an advancing step to cover the face of the crystal. The thickness, number density, and frequency of formation of layer nuclei increase with supersaturation. To nucleate a layer requires a higher supersaturation than to make it spread. Figure 6 is a photograph of the growing surface of a diamond crystal. The growth layers, a few microns thick, are typical. The layers originate from nucleation sites which usually lie near the edges of a crystal; these edges represent the vestiges of the most rapidgrowring or easily nucleated crystal faces, as determined mainly by chemical bonding densities. The advancing layer step perpetuates itself because its base or inside corner cannot advance as rapidly as the top corner. The top comer region has a better supply of fresh carbon atoms and the inside comer has a higher concentration of impurities accumulated in front of the advancing step. (See Figure 7.) The desorption and diffusing away of these impurities probably are the limiting rate factors in growing sound crystals. If the carbon is supplied too rapidly, the step is roofed over, and impurities and bath are trapped in the crystal. Usually a growing crystal face bears many “difficult” regions over which new growth proceeds very reluctantly and near which growth layer steps tend t o pile up. To avoid trapping impurities a t such regions, new layers must not be nucleated faster than old ones are completed. If the area of difficult regions remained constant, regardless of crystal size, then the allowable radial growth rate of large crystals would be the same as for small crystals and would be much higher than is observed. However, if the area of difficult regions were proportional to the face area, then the time for a layer to traverse the face would be proportional to the face size, and since the growth layers seem to be all about the same thickness, the radial growth rate of the crystal would be inversely proportional to its average diameter. Out of many experiments on diamond growth, some happened to be conducted at the maximum sound growth rate for the particular size crystal obtained, and a consideration of these data supports the analysis given above, although perhaps other growth mechanisms The Jwrnal of Phv&
Chnnblry. Vol. 76. No. I d . 1871
\
\
Figure 6. Photomicrograph (3.Wx)of growing surfitre of diamond crystal, showing stepped layers of growth.
Figure I. Sketch of processes occurring near a growth step.
could operate to produce the same result. may write
Thus one
2wb = 1
where s is an average diameter, in mm, of the crystal; r is the maximum sound growth rate, in mm/hr; b is 8 parameter related to the particular conditions of growth. I n this study, b often appeam to be about 2.5 hr mm-*. It vanes somewhat for different baths. Then the time to p o w to a size L , growing always as fast as possible, is L
T(L)=
ds/r = 0
1‘
2 b d s = bL*
From this expression one may deduce that a highquality, inclusion-free 3-mm crystal requires 22.5 hr, or a 6-mm crystal 90 hr, in typical transition metalcatalyst systems. In practice it is not simple to adjust the supersaturation and layer nucleation and growth rates continuously 80 as to match the crystal size, and it is easier to
SOMESTUDIES OF DIAMOND GROWTH RATES grow the entire crystal a t a rate set by the final size. Then one finds that a 3-mm crystal would require about 55 hr, a 5-mm crystal 167 hr, etc. These values agree generally with experience in our laboratory; i.e., a 5mm (1 carat) gem quality crystal can be grown in about a week. The value of the parameter b changes slightly with the composition of the bath. It would also be expected to fall with increasing temperature as impurity diffusion would be hastened, but the limited temperature range available to us in these studies has not permitted confirmation on this point. So far the average growth rates for diamond appear to be slightly below those obtained for quartz, garnets, ZnS, etc., from molten solvent systems. 6. Chemical Efects. More or less controlled amounts of certain im1:urities may be added to the bath by alloying them with the bath metal or placing them between the metal and nutrient. Many interesting reactions and effects may occur. For example, Ca or Sr are converted to their carbides and may gather some nitrogen as cyanamides. Other active metals such as Ti or Cr tend to form carbides-which may crystallize in the cool end of the bath and oxides, etc., which are more insoluble. Easily reduced oxides such as Fe304 are reduced and the product CO diffuses about in the cell. Si or A1 can combine with excess 0 or reduce CO. S or P simply dissolve in the bath. It is difficult to be sure about anything with H because of its
1837 extreme mobility. Nitrogen is taken up by the growing diamond. Ordinary carbon, iron, nickel, etc. contain enough nitrogen to color the diamond yellow and produce other effects in the crystals. Excess nitrogen added as azide, cyanide, melamine, etc., produces green diamonds. Too much nitrogen, oxygen, or sulfur seriously interferes with diamond growth. Zr, Ti, or A1 combine with N and the resulting diamonds are colorless. B also combines with N but the resulting diamonds are blue and semiconducting.'l Either B or A1 can be incorporated into growing diamonds in limited amounts depending, in part, on their concentration in the melt. Although some of these diamond-growing baths appear to be chemically more pure than those in nature, it is very difficult to approach semiconductor standards of purity currently achieved in intrinsic silicon or germanium. Fortunately, the growing diamond does not always accept all the impurities present. 6. Further Considerations. At the moment it is not economical to use this method to grow gem crystals for sale. However, the method is technologically useful for growing many interesting kinds of diamond crystals in sizes large enough for studies of their properties.
Acknowledgment. I wish to express my thanks to W. A. Rocco for his help in this work. (11) R. H. Wentorf, Jr., and H. P. Bovenkerk, J . Chem. Phys., 36, 1987 (1962).
The Journal of Physical Chemistry, Vol. 76,No. 19,1871
